Saturday, August 04, 2007

Bad Statistical Inferences

As a general rule, people are not too good at making statistical inferences. This is obvious from the fact that lottery tickets sell so well. As a matter of fact (and not too many people are aware of this fact), buying a lottery ticket does not statistically significantly increase one's chances of winning. Why is this you might ask. Think about it for a moment.

Suppose the odds of winning on a particular lottery is in the order of one in 32 million. Buying a ticket thus increases one's chance of winning by one thirty-second of a million. This amount is so small that it falls below the level of statistical significance. This is the reason why this fact about lottery tickets is the case.

One can see something similar in games of chance. Consider Roulette. If one observes people playing Roulette, or even hears someone talking about playing, they will say things like "Red has got to come up soon!" Unfortunately, this is not true. For any particular spin of the wheel, the chances of the ball landing on red is just a little below 50% (it is a little below, due to 0 and 00). Even if red has not come up for a number of spins, this fact does not change. The chance is a little below 50% for each spin of the wheel. The wheel has no memory. So, the results of previous spins have no influence upon the next one.

Something similar applies to coin tosses. I just tossed a coin three times. On each occasion, it came up tails. Suppose you were asked to bet on the outcome of the next toss of the coin. Some people would be tempted to guess that the next toss would yield the result heads, as it was 'due to come up'. Of course, this is rubbish. As a matter of fact, when I tossed the coin for a fourth time, the result was another tails. Actually, heads did not come up until the eighth toss of the coin. The coin also came up heads on the ninth and tenth toss.

These facts help to illustrate another salient fact. Out of ten coin tosses, seven came up tails and only three came up heads. However, we know that the chance of one side or the other coming up is 50%. What these results help illustrate is that the chance of a particular side coming up is 50% on average. With a small number of tosses, like just ten, this statistical fact is of little relevance to predicting the actual behavior of the coin.

You might wonder why I am bothering discussing statistical inferences and the problems that they can give rise to, at all. What motivates me here is an especially poor example of statistical inference that has been annoying me in a television commercial.

On certain channels, at certain times, there is a commercial for the medication Valtrex. Apparently, Valtrex helps to suppress genital herpes. Presumably, the goal of the commercial is to persuade sufferers of this affliction to ask their physicians to prescribe Valtrex. However, the way the commercial makers go about achieving this goal involves some especially shoddy and misleading statistical inference.

At one point in the commercial, the voice over reads a caption that is also shown on the screen. The text here informs the viewer that,

"One study found that up to 70% of people who had genital herpes got it from their partners when they had no signs of an outbreak."

This sounds pretty worrying doesn't it? However, look at the claim a little more closely and the dubious slight of hand that is being pull off here becomes obvious.

Consider the following questions: If only 'one study' found this result, what did the other studies find? How large was the sample size of the cited study? Were the people looked at in this study picked at random? Where was this 'study' published? Who conducted this study? Without some answers to these questions, this supposed statistical 'fact' is close to being meaningless. In all likelihood, the manufacturers 'cherry picked' this result to maximise the chances of selling their product. With so little information provided, it is almost always possible to conduct a 'study' to produce whatever results one wishes.

As a matter of fact, this so-called 'fact' does little more than create what is sometime called FUD - "Fear, Uncertainty and Doubt". Notice though that by using the term 'study' and citing a putative statistical value, this claim attempts to convey the authority of science. In reality, witchcraft is about as trustworthy.

To make matters worse, after the presentation of the above quoted claim, an actor offers an interpretation for the viewer that is even more confusing. They say,

"This means that I could pass on herpes at any time."

Once again, this is palpable nonsense, even if one accepts the statistical claims as being reliable. Again, the goal appears to drive home FUD.

It seems to me that this commercial is at the very least irresponsible. It plays upon people's poor skills at statistical inference. To make matters worse, this is a claim that is being promoted by a pharmaceutical company. As this type of corporation has to rely upon statistical evidence when evaluating the safety and effectiveness of their products, the statistical confusion presented in this commercial suggests that they should not be trusted at all.

The CP

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